If you go to about:config and then create a new boolean for extensions.checkCompatibility.13.0 and set it to false there is a good chance it will work. I know it does for 5.x. If I have time I will try it this weekend since I got my test computer back up and running that has the 6.x beta.

I just checked in Firefox Aurora 14.0a2 and the Firefox Nightly 15.0a1 as well as Firefox 13.0b3. Sticky Password 6 beta works in all of them. Do the following for each version:

Firefox 13.0b3add boolean extensions.checkCompatibility.13.0 and set to false

Firefox Aurora 14.0a2add boolean extensions.checkCompatibility.14.0a and set to false

Firefox Aurora 15.0a1add boolean extensions.checkCompatibility.15.0a and set to false

This is the way around the current limitations. I have not seen an issue with doing this. Remember however using these versions means you might encounter unforeseen issues due to less testing. That said the beta feels pretty much production ready. They all feel faster than the current release 12.0 version. Enjoy.